AI & ChatGPT searches , social queries for DIRICHLET SPACE
Search references for DIRICHLET SPACE. Phrases containing DIRICHLET SPACE
See searches and references containing DIRICHLET SPACE!
Search references for DIRICHLET SPACE. Phrases containing DIRICHLET SPACE
See searches and references containing DIRICHLET SPACE!DIRICHLET SPACE
In mathematics, the Dirichlet space on the domain Ω ⊆ C , D ( Ω ) {\displaystyle \Omega \subseteq \mathbb {C} ,\,{\mathcal {D}}(\Omega )} (named after
Dirichlet_space
Probability distribution
In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir ( α ) {\displaystyle \operatorname
Dirichlet_distribution
Type of constraint on solutions to differential equations
In mathematics, the Dirichlet boundary condition is imposed on an ordinary or partial differential equation, such that the values that the solution takes
Dirichlet_boundary_condition
Mathematical form
analysis, Dirichlet forms generalize the Laplacian (the mathematical operator on scalar fields). Dirichlet forms can be defined on any measure space, without
Dirichlet_form
number theory) Dirichlet series inversion General Dirichlet series Dirichlet space Dirichlet stability criterion (dynamical systems) Dirichlet tessellation
List of things named after Peter Gustav Lejeune Dirichlet
List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
Mathematical measure of a function's variability
the Dirichlet energy is a measure of how variable a function is. More abstractly, it is a quadratic functional on the Sobolev space H1. The Dirichlet energy
Dirichlet_energy
Type of plane partition
Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons
Voronoi_diagram
Problem of solving a partial differential equation subject to prescribed boundary values
In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region
Dirichlet_problem
If there are more items than boxes holding them, one box must contain at least two items
commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the
Pigeonhole_principle
spaces", Encyclopedia of Mathematics, EMS Press. Bergman kernel Banach space Hilbert space Reproducing kernel Hilbert space Hardy space Dirichlet space
Bergman_space
Family of stochastic processes
In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes
Dirichlet_process
Vector space of functions in mathematics
consisting of eigenvectors of the Laplace operator (with Dirichlet boundary condition). Sobolev spaces are often considered when investigating partial differential
Sobolev_space
Type of vector space in math
plane and three-dimensional space to spaces of any finite or infinite dimension. A Hilbert space is an abstract vector space, and it has the additional
Hilbert_space
Model for representing text documents
document frequency, latent semantic indexing, random projections and latent Dirichlet allocation. Weka. Weka is a popular data mining package for Java including
Vector_space_model
Concept in mathematical analysis
In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n
Dirichlet_kernel
Integral of sin(x)/x from 0 to infinity
are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral
Dirichlet_integral
Test for series convergence
In mathematics, Dirichlet's test is a method of testing for the convergence of a series that is especially useful for proving conditional convergence
Dirichlet's_test
(pseudo-)Riemannian manifold whose geodesics are reversible
symmetric riemannian spaces, with applications to Dirichlet series", J. Indian Math. Society, 20: 47–87 Wolf, Joseph A. (1999), Spaces of constant curvature
Symmetric_space
Type of mathematical space
point of the space—and to extend it to information that holds globally throughout the space. An example of this phenomenon is Dirichlet's theorem, to which
Compact_space
Space of all possible states that a system can take
The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible
Phase_space
Second-order partial differential equation
relative to the new coordinates and Γ denotes its Christoffel symbols. The Dirichlet problem for Laplace's equation consists of finding a solution φ on some
Laplace's_equation
Modes of vibration in mathematics
In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can
Dirichlet_eigenvalue
Method of mathematical integration
polynomials. However, the graphs of other functions, for example the Dirichlet function, do not fit well with the notion of area. Graphs like that of
Lebesgue_integral
Differential calculus on function spaces
equation satisfy the Dirichlet's principle. Plateau's problem requires finding a surface of minimal area that spans a given contour in space: a solution can
Calculus_of_variations
Statistical Markov model
two-level prior Dirichlet distribution, in which one Dirichlet distribution (the upper distribution) governs the parameters of another Dirichlet distribution
Hidden_Markov_model
Mathematics theorem
various function spaces of holomorphic functions on the disk. These spaces include the Hardy spaces, the Bergman spaces and Dirichlet space. Let h be a holomorphic
Littlewood subordination theorem
Littlewood_subordination_theorem
Extended objects found in string theory
theory, D-branes, short for Dirichlet membrane, are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after
D-brane
Canadian mathematician
El-Fallah, K. Kellay, J. Mashreghi, T. Ransford, A Primer on the Dirichlet Space, Cambridge Tracts in Mathematics 203, Cambridge University Press, Cambridge
Javad_Mashreghi
Monte Carlo algorithm
as latent Dirichlet allocation and various other models used in natural language processing, it is quite common to collapse out the Dirichlet distributions
Gibbs_sampling
Function which is not continuous at any point of its domain
is the indicator function of the rational numbers, also known as the Dirichlet function. This function is denoted as 1 Q {\displaystyle \mathbf {1} _{\mathbb
Nowhere_continuous_function
Multivariate derivative (mathematics)
increase. The gradient transforms like a vector under change of basis of the space of variables of f {\displaystyle f} . If the gradient of a function is non-zero
Gradient
Formula in number theory
the coefficients of the Dirichlet series representation of the Dedekind zeta function. The n-th coefficient of the Dirichlet series is essentially the
Class_number_formula
Type of problem involving ODEs or PDEs
studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation); the solution was given by the Dirichlet's principle
Boundary_value_problem
Conditions for switching order of integration in calculus
{\pi }{2}}\ln(2)\end{aligned}}} The Dirichlet series defines the Dirichlet eta function as follows: η ( s ) = ∑ n = 1 ∞ ( − 1 ) n −
Fubini's_theorem
Conjecture on zeros of the zeta function
and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series", J. Indian Math. Soc., New Series, 20: 47–87, MR 0088511
Riemann_hypothesis
Statement relating differentiable symmetries to conserved quantities
action. This theorem applies to continuous and smooth symmetries of physical space. Noether's formulation is quite general and has been applied across classical
Noether's_theorem
German mathematician
local Dirichlet spaces – III. Journal de Mathématiques Pures et Appliquées 75 (1996), 273–297. Sturm, K.-T. Analysis on local Dirichlet spaces – II. Osaka
Karl-Theodor_Sturm
Derivative defined on normed spaces
In mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative
Fréchet_derivative
French mathematician
“I see, yes, those are very hard problems”. The analytic parts of Dirichlet space theory have played an enormous role in my recent work. I am sure that
Paul-André_Meyer
Infinite sum
Like the zeta function, Dirichlet series in general play an important role in analytic number theory. Generally a Dirichlet series converges if the real
Series_(mathematics)
German mathematician (1826–1866)
During his time of study, Carl Gustav Jacob Jacobi, Peter Gustav Lejeune Dirichlet, Jakob Steiner, and Gotthold Eisenstein were teaching. He stayed in Berlin
Bernhard_Riemann
Theorem in vector calculus
theorem in vector calculus on three-dimensional Euclidean space and real coordinate space, R 3 {\displaystyle \mathbb {R} ^{3}} . Given a vector field
Stokes'_theorem
Algebraic structure
In mathematics, a Dirichlet algebra is a particular type of algebra associated to a compact Hausdorff space X. It is a closed subalgebra of C(X), the
Dirichlet_algebra
Stochastic process in probability theory
θ > −d and a base distribution G0 over a probability space X. When d = 0, it becomes the Dirichlet process. The discount parameter gives the Pitman–Yor
Pitman–Yor_process
Differential operator in mathematics
underlying space. A version of the Laplacian can be defined wherever the Dirichlet energy functional makes sense, which is the theory of Dirichlet forms.
Laplace_operator
Sobolev spaces for planar domains are one of the principal techniques used in the theory of partial differential equations for solving the Dirichlet and Neumann
Sobolev spaces for planar domains
Sobolev_spaces_for_planar_domains
Mathematics
is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed
Neumann_boundary_condition
Matrix of partial derivatives of a vector-valued function
Direct comparison Limit comparison Alternating series Cauchy condensation Dirichlet Abel Vector Gradient Divergence Curl Laplacian Directional derivative
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Formula in calculus
is an operation on spaces and functions between them. It associates to each space a new space and to each function between two spaces a new function between
Chain_rule
Certain vector fields are the sum of an irrotational and a solenoidal vector field
three-dimensional space, this is equivalent to the rotation of the vector potential. In a d {\displaystyle d} -dimensional vector space with d ≠ 3 {\displaystyle
Helmholtz_decomposition
Analytic function in mathematics
Many generalizations of the Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known. The Riemann zeta function
Riemann_zeta_function
Probability distribution
In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and
Generalized Dirichlet distribution
Generalized_Dirichlet_distribution
Mathematical function with no sudden changes
1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. A real function, that is, a function from real numbers to real
Continuous_function
Mathematical operation
transform. This integral transform is closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and
Mellin_transform
Differentiation under the integral sign formula
_{0}^{1}{\frac {x^{\alpha }-1}{\ln x}}dx.\end{aligned}}} The first integral, the Dirichlet integral, is absolutely convergent for positive α but only conditionally
Leibniz_integral_rule
Operation in mathematical calculus
connecting two points in space. In a surface integral, the curve is replaced by a piece of a surface in three-dimensional space. The first documented systematic
Integral
Portuguese mathematician (born 1956)
Mathematics: Bulletin 26 (2), (2011) "Composition Operators on a Local Dirichlet Space", (with D Sarason), J. Ana. Math. 87, 433-450 Breakfast with John Horton
Jorge_Nuno_Silva
Instantaneous rate of change (mathematics)
{\displaystyle M} is a space that can be approximated near each point x {\displaystyle x} by a vector space called its tangent space: the prototypical example
Derivative
Mathematical concept
kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disk. The kernel can be understood as
Poisson_kernel
Polygon associated with a compact Riemann surface
convex polygon for the hyperbolic metric on H. These can be defined by Dirichlet polygons and have an even number of sides. The structure of the fundamental
Fundamental_polygon
Concept in mathematics
also arises as the Euler-Lagrange equation of a functional called the Dirichlet energy. As such, the theory of harmonic maps contains both the theory
Harmonic_map
Gives the rank of the group of units in the ring of algebraic integers of a number field
In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of
Dirichlet's_unit_theorem
On converting relations to functions of several real variables
Discusses Implicit function Theorem for X a topological space , Y Banach Space, Z a Topological Vector space Allendoerfer, Carl B. (1974). "Theorems about Differentiable
Implicit_function_theorem
Circulation density in a vector field
infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length
Curl_(mathematics)
Generalized function whose value is zero everywhere except at zero
integrals only converge in the sense of distributions (an example is the Dirichlet kernel below), rather than in the sense of measures. Another example is
Dirac_delta_function
Calculus of functions generalization
on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean space R n {\displaystyle
Calculus_on_Euclidean_space
Formal power series
Bell series, and Dirichlet series. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require
Generating_function
Generalization of the concept of directional derivative
between locally convex topological vector spaces such as Banach spaces. Like the Fréchet derivative on a Banach space, the Gateaux differential is often used
Gateaux_derivative
Matrix of second derivatives
blob detector, the determinant of Hessian (DoH) blob detector and scale space). It can be used in normal mode analysis to calculate the different molecular
Hessian_matrix
Mathematical techniques used in probability theory and related fields
variations. P. Malliavin first initiated the calculus on infinite dimensional space. Then, significant contributors such as S. Kusuoka, D. Stroock, J-M. Bismut
Malliavin_calculus
Theorem in mathematics
(of real or complex numbers) to n-tuples, and to functions between vector spaces of the same finite dimension, by replacing "derivative" with "Jacobian matrix"
Inverse_function_theorem
British scientist (born 1958)
the Complex Plane" in 1995, and the graduate book "A Primer on the Dirichlet Space" with Omar El-Fallah, Karim Kellay and Javad Mashreghi in 2014 [1]
Thomas_Ransford
Branch of number theory
Lejeune Dirichlet's work was what led him to his later study of algebraic number fields and ideals. In 1863, he published Lejeune Dirichlet's lectures
Algebraic_number_theory
Function that is discontinuous at rationals and continuous at irrationals
function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function (not to be confused with the integer ruler
Thomae's_function
Generalization of Voronoi diagrams
the multiplicatively weighted Voronoi diagram is also called circular Dirichlet tessellation and its edges are circular arcs and straight line segments
Weighted_Voronoi_diagram
Type of space-filling polyhedron
doi:10.2307/3616930, JSTOR 3616930. Schmitt, Moritz (2016), On Space Groups and Dirichlet-Voronoi Stereohedra, doi:10.17169/refubium-14374. Erickson, Jeff;
Plesiohedron
Extended physical object in string theory
required to lie on a D-brane. The letter "D" in D-brane refers to the Dirichlet boundary condition, which the D-brane satisfies. One crucial point about
Brane
Mathematical notion of infinitesimal difference
dimension, any inner product space is a Hilbert space, any normed vector space is a Banach space and any topological vector space is complete. As a result
Differential_(mathematics)
Vector operator in vector calculus
there are more of the field vectors exiting from an infinitesimal region of space than entering it. A point at which the flux is outgoing has positive divergence
Divergence
Inputs for which a function's value is non-zero
if f : [ 0 , 1 ] → R {\displaystyle f:[0,1]\to \mathbb {R} } is the Dirichlet function that is 0 {\displaystyle 0} on irrational numbers and 1 {\displaystyle
Support_(mathematics)
Summability method in physics
to any sums over an arithmetic function f(n). Such sums are known as Dirichlet series. The regularized form f ~ ( s ) = ∑ n = 1 ∞ f ( n ) n − s {\displaystyle
Zeta_function_regularization
Vector calculus formulas relating the bulk with the boundary of a region
is chosen to be Green's function that vanishes on the boundary of U (Dirichlet boundary condition), ∮ ∂ U ψ ( y ) ∂ G ( y , η ) ∂ n d S y = { ψ ( η )
Green's_identities
special case of Dirichlet series. Riemann Xi function Dirichlet eta function: An allied function. Dirichlet beta function Dirichlet L-function Hurwitz
List of mathematical functions
List_of_mathematical_functions
Infinite series summing alternating 1 and -1 terms
limits of the Dirichlet, Fejér, and Poisson kernels, respectively. Multiplying the terms of Grandi's series by 1/nz yields the Dirichlet series η ( z )
Grandi's_series
Boundary condition for generalized functions
consider the problem of solving Poisson's equation with inhomogeneous Dirichlet boundary conditions: − Δ u = f in Ω , u = g on ∂ Ω {\displaystyle
Trace_operator
Method for constructing existence proofs and calculating solutions in variational calculus
conditions. This is similar to solving the Euler–Lagrange equation with Dirichlet boundary conditions. Additionally there are settings in which there are
Direct method in the calculus of variations
Direct_method_in_the_calculus_of_variations
Numerical method for solving physical or engineering problems
with respect to x {\displaystyle x} . P2 is a two-dimensional problem (Dirichlet problem) P2 : { u x x ( x , y ) + u y y ( x , y ) = f ( x , y ) in
Finite_element_method
Counting technique in combinatorics
} The Dirichlet hyperbola method re-expresses a sum of a multiplicative function f ( n ) {\displaystyle f(n)} by selecting a suitable Dirichlet convolution
Inclusion–exclusion_principle
Formula for the derivative of a product
\\[-3ex]&\end{aligned}}} Suppose X, Y, and Z are Banach spaces (which includes Euclidean space) and B : X × Y → Z is a continuous bilinear operator. Then
Product_rule
trial data with a Dirichlet prior requires only adding the outcome frequencies to the Dirichlet prior alpha values, resulting in a Dirichlet posterior distribution
Expected value of sample information
Expected_value_of_sample_information
Mathematical operation
example, assuming x ∈ [ 0 , L ] {\displaystyle x\in [0,L]} and homogeneous Dirichlet boundary conditions (i.e., v ( 0 ) = v ( L ) = 0 {\displaystyle v(0)=v(L)=0}
Second_derivative
Integral transform useful in probability theory, physics, and engineering
to compute using elementary methods of real calculus. For example, the Dirichlet integral can be evaluated using the Laplace transform: ∫ 0 ∞ sin x x
Laplace_transform
Technique in integral evaluation
be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be a σ-compact Hausdorff space with a σ-finite Radon measure ρ
Integration_by_substitution
Discrete probability distribution
and multinomial distributions can lead to problems. For example, in a Dirichlet-multinomial distribution, which arises commonly in natural language processing
Categorical_distribution
Geometry notion in mathematics
and discontinuous groups in weakly symmetric riemannian spaces, with applications to Dirichlet series", J. Indian Math. Society, 20: 47–87 Stembridge,
Weakly_symmetric_space
Iterative method in conformal mapping
plane in each of which the Dirichlet problem could be solved, Schwarz described an iterative method for solving the Dirichlet problem in their union, provided
Schwarz_alternating_method
Branch of mathematical analysis
tail decay and the spatial derivative for diffusion nonlocality. The time-space fractional diffusion governing equation can be written as ∂ α u ∂ t α =
Fractional_calculus
Theorem in measure theory
the first n rationals and 0 otherwise. Then f {\displaystyle f} is the Dirichlet function on [ 0 , 1 ] {\displaystyle [0,1]} , which is not Riemann integrable
Dominated_convergence_theorem
Mathematical identities
algebra relations – Formulas about vectors in three-dimensional Euclidean space Wilson, p. 404. Wilson, p. 407. Wilson, p. 407. Coffin, Joseph George (1911)
Vector_calculus_identities
Subset of Euclidean space is compact if and only if it is closed and bounded
closed and bounded interval is uniformly continuous. Peter Gustav Lejeune Dirichlet was the first to prove this and implicitly he used the existence of a
Heine–Borel_theorem
DIRICHLET SPACE
DIRICHLET SPACE
Boy/Male
Hindu
Space
Boy/Male
Hindu
Space
Surname or Lastname
English
English : habitational name from either of two places in Cheshire. It is possible that the name originally denoted a building where village assemblies were held, named in Old English as ‘meeting-house’, from (ge)mÅt ‘meeting’ + ærn ‘house’, ‘hall’. Other possibilities are that the name derives from Old English (ge)mÅt-rÅ«m ‘meeting space’, or (ge)mÅt-treum ‘assembly trees’.
Boy/Male
Arabic, Muslim, Pashtun
Battle Field; Open Space
Girl/Female
Gujarati, Hindu, Indian
Star in Space
Girl/Female
Indian, Telugu
Space
Boy/Male
Muslim
Open space, Battle field
Boy/Male
Hindu
Limitless space Avatar incarnation
Girl/Female
Maori
Open spaces.
Girl/Female
Indian, Telugu
Goddess of Space
Girl/Female
Biblical
Spaces, places.
Boy/Male
Biblical
Breadth, space, extent.
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
Boy/Male
Hindu
Space
Boy/Male
Tamil
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Space
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Boy/Male
Tamil
Limitless space Avatar incarnation
Boy/Male
Indian
Open space, Battle field
Girl/Female
Indian, Japanese, Tamil
Space; Star
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
DIRICHLET SPACE
DIRICHLET SPACE
Boy/Male
Indian, Sanskrit
Jewel of the Day; Sun
Girl/Female
Indian
Morning Friend
Boy/Male
Hindu, Indian, Marathi
Powerful; Radiant
Boy/Male
Sikh
One with divine knowledge, Victory of the gem
Boy/Male
Tamil
Talented
Boy/Male
British, English
Red Wolf
Boy/Male
Arabic, Muslim, Sindhi
Gift; Inherent; Giving Donation; Grant
Boy/Male
American, Australian, British, English, French
Darling; Beloved; Open; Variant of Darrel Open
Girl/Female
Greek
A vision.
Girl/Female
Tamil
Ayurdha | அயà¯à®°à¯à®¤à®¾
Bestowed of longevity
DIRICHLET SPACE
DIRICHLET SPACE
DIRICHLET SPACE
DIRICHLET SPACE
DIRICHLET SPACE
n.
Rate of motion; the relation of motion to time, measured by the number of units of space passed over by a moving body or point in a unit of time, usually the number of feet passed over in a second. See the Note under Speed.
a.
Without space.
n.
One who holds the doctrine that the space between the bodies of the universe, or the molecules and atoms of matter., is a vacuum; -- opposed to plenist.
n.
The space inclosed between ranges of hills or mountains; the strip of land at the bottom of the depressions intersecting a country, including usually the bed of a stream, with frequently broad alluvial plains on one or both sides of the stream. Also used figuratively.
n.
Space unfilled or unoccupied, or occupied with an invisible fluid only; emptiness; void; vacuum.
n.
A small air cell, or globular space, in the interior of organic cells, either containing air, or a pellucid watery liquid, or some special chemical secretions of the cell protoplasm.
n.
To arrange or adjust the spaces in or between; as, to space words, lines, or letters.
n.
An empty space; a vacuum.
imp. & p. p.
of Space
n.
A border, limit, or boundary of a space; an edge, margin, or brink of something definite in extent.
a.
Having the inner part cut away, or left vacant, a narrow border being left at the sides, the tincture of the field being seen in the vacant space; -- said of a charge.
n.
A waste region; boundless space; immensity.
n.
Dimensions; compass; space occupied, as measured by cubic units, that is, cubic inches, feet, yards, etc.; mass; bulk; as, the volume of an elephant's body; a volume of gas.
n.
A quantity or portion of extension; distance from one thing to another; an interval between any two or more objects; as, the space between two stars or two hills; the sound was heard for the space of a mile.
n.
The circular membrane that partially incloses the space beneath the umbrella of hydroid medusae.
n.
A forest officer appointed to walk over a certain space for inspection; a forester.
n.
A space entirely devoid of matter (called also, by way of distinction, absolute vacuum); hence, in a more general sense, a space, as the interior of a closed vessel, which has been exhausted to a high or the highest degree by an air pump or other artificial means; as, water boils at a reduced temperature in a vacuum.
n.
Intermission of judicial proceedings; the space of time between the end of one term and the beginning of the next; nonterm; recess.
n.
That which is near, or not remote; that which is adjacent to anything; adjoining space or country; neighborhood.
n.
An open or unoccupied space between bodies or things; an interruption of continuity; chasm; gap; as, a vacancy between buildings; a vacancy between sentences or thoughts.